Olber's Paradox assumes that the universe is infinite in size, that space is 100% transparent, that matter is uniformly distributed throughout, and that it is static and infinite in age. We call this a Newtonian Universe. It was a reasonable assumption based on what was known about the universe before the 20th century. I don't think astronomers figured out what galaxies were until sometime in the early 20th century. Once it was realised that the sun is just another star, the natural assumption was that stars were scattered randomly and uniformly throughout the universe. Olber's Paradox makes that assumption impossible.
If you move a star twice as far away from an observer, he or she will intercept one quarter as many photons, but the star will subtend one quarter of the angular area. So the areal intensity from the observer's point of view remains constant.
The reason that the light from a distant star the same size and temperature as the sun, is fainter that the light from our sun, is that that the angular area subtended by the distant star as viewed from the earth is enormously smaller. In addition, we now know that some of the light from the distant star is absorbed by random gas and dust molecules in space.
The Paradox says that in an infinite, transparent universe, with an infinite number of stars, there would eventually be a star somewhere no matter what direction the observer might look, just as there is eventually a tree somewhere in every direction an observer looks in a deep forest. Thus the areal intensity of any arbitrarily defined segment of the sky should be at least as intense the surface of a star, and the whole sky should be alaze with light as intense as the sun. This would make the entire universe one huge firestorm.
The paradox is solved by changing the assumption to a universe that is finite in size and that had a finite moment of creation. In addition, radiation from far away stars and matter is shielded by closer by stars and matter, so space is not absolutely transparent.
But here's another solution that does not require rejecting any of Olber’s basic assumptions
of the universe.
Olber’s Paradox Solved
